FINITE-ELEMENT ANALYSIS OF TIME-DEPENDENT CONVECTION DIFFUSION EQUATIONS (PETROV-GALERKIN).
Petrov-Galerkin finite element methods based on time-space elements are developed for the time-dependent multi-dimensional linear convection-diffusion equation. The methods introduce two parameters in conjunction with perturbed weighting functions. These parameters are determined locally using trunc...
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The University of Arizona.
1986
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ndltd-arizona.edu-oai-arizona.openrepository.com-10150-1839302015-10-23T04:28:52Z FINITE-ELEMENT ANALYSIS OF TIME-DEPENDENT CONVECTION DIFFUSION EQUATIONS (PETROV-GALERKIN). YU, CHUNG-CHYI. Heinrich, Juan C. Pearlstein, Arne J. Chen, C. F. Heat -- Convection -- Mathematical models. Diffusion -- Mathematical models. Fluid mechanics -- Mathematical models. Finite element method. Petrov-Galerkin finite element methods based on time-space elements are developed for the time-dependent multi-dimensional linear convection-diffusion equation. The methods introduce two parameters in conjunction with perturbed weighting functions. These parameters are determined locally using truncation error analysis techniques. In the one-dimensional case, the new algorithms are thoroughly analyzed for convergence and stability properties. Numerical schemes that are second order in time, third order in space and stable when the Courant number is less than or equal to one are produced. Extensions of the algorithm to nonlinear Navier-Stokes equations are investigated. In this case, it is found more efficient to use a Petrov-Galerkin method based on a one parameter perturbation and a semi-discrete Petrov-Galerkin formulation with a generalized Newmark algorithm in time. The algorithm is applied to the two-dimensional simulation of natural convection in a horizontal circular cylinder when the Boussinesq approximation is valid. New results are obtained for this problem which show the development of three flow regimes as the Rayleigh number increases. Detailed calculations for the fluid flow and heat transfer in the cylinder for the different regimes as the Rayleigh number increases are presented. 1986 text Dissertation-Reproduction (electronic) http://hdl.handle.net/10150/183930 697842025 8702358 en Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. The University of Arizona. |
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NDLTD |
language |
en |
sources |
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topic |
Heat -- Convection -- Mathematical models. Diffusion -- Mathematical models. Fluid mechanics -- Mathematical models. Finite element method. |
spellingShingle |
Heat -- Convection -- Mathematical models. Diffusion -- Mathematical models. Fluid mechanics -- Mathematical models. Finite element method. YU, CHUNG-CHYI. FINITE-ELEMENT ANALYSIS OF TIME-DEPENDENT CONVECTION DIFFUSION EQUATIONS (PETROV-GALERKIN). |
description |
Petrov-Galerkin finite element methods based on time-space elements are developed for the time-dependent multi-dimensional linear convection-diffusion equation. The methods introduce two parameters in conjunction with perturbed weighting functions. These parameters are determined locally using truncation error analysis techniques. In the one-dimensional case, the new algorithms are thoroughly analyzed for convergence and stability properties. Numerical schemes that are second order in time, third order in space and stable when the Courant number is less than or equal to one are produced. Extensions of the algorithm to nonlinear Navier-Stokes equations are investigated. In this case, it is found more efficient to use a Petrov-Galerkin method based on a one parameter perturbation and a semi-discrete Petrov-Galerkin formulation with a generalized Newmark algorithm in time. The algorithm is applied to the two-dimensional simulation of natural convection in a horizontal circular cylinder when the Boussinesq approximation is valid. New results are obtained for this problem which show the development of three flow regimes as the Rayleigh number increases. Detailed calculations for the fluid flow and heat transfer in the cylinder for the different regimes as the Rayleigh number increases are presented. |
author2 |
Heinrich, Juan C. |
author_facet |
Heinrich, Juan C. YU, CHUNG-CHYI. |
author |
YU, CHUNG-CHYI. |
author_sort |
YU, CHUNG-CHYI. |
title |
FINITE-ELEMENT ANALYSIS OF TIME-DEPENDENT CONVECTION DIFFUSION EQUATIONS (PETROV-GALERKIN). |
title_short |
FINITE-ELEMENT ANALYSIS OF TIME-DEPENDENT CONVECTION DIFFUSION EQUATIONS (PETROV-GALERKIN). |
title_full |
FINITE-ELEMENT ANALYSIS OF TIME-DEPENDENT CONVECTION DIFFUSION EQUATIONS (PETROV-GALERKIN). |
title_fullStr |
FINITE-ELEMENT ANALYSIS OF TIME-DEPENDENT CONVECTION DIFFUSION EQUATIONS (PETROV-GALERKIN). |
title_full_unstemmed |
FINITE-ELEMENT ANALYSIS OF TIME-DEPENDENT CONVECTION DIFFUSION EQUATIONS (PETROV-GALERKIN). |
title_sort |
finite-element analysis of time-dependent convection diffusion equations (petrov-galerkin). |
publisher |
The University of Arizona. |
publishDate |
1986 |
url |
http://hdl.handle.net/10150/183930 |
work_keys_str_mv |
AT yuchungchyi finiteelementanalysisoftimedependentconvectiondiffusionequationspetrovgalerkin |
_version_ |
1718097219725295616 |